Different methods of constructing potential energy surfaces in polyatomic systems are reviewed, with the emphasis put on fitting, interpolation, and analytical (defined by functional forms) approaches, based on quantum chemistry electronic structure calculations. The different approaches are reviewed first, followed by a comparison using the benchmark H + CH_{4} and the H + NH_{3} gas-phase hydrogen abstraction reactions. Different kinetics and dynamics properties are analyzed for these reactions and compared with the available experimental data, which permits one to estimate the advantages and disadvantages of each method. Finally, we analyze different problems with increasing difficulty in the potential energy construction: spin-orbit coupling, molecular size, and more complicated reactions with several maxima and minima, which test the soundness and general applicability of each method. We conclude that, although the field of small systems, typically atom-diatom, is mature, there still remains much work to be done in the field of polyatomic systems.

At the heart of chemistry lies the knowledge of the reaction mechanism at atomic or molecular levels, that is, the motion of the nuclei in the potential field due to the electrons and nuclei. When the separation of the nuclear and electronic motions is possible, that is, within the Born-Oppenheimer (BO) approximation [

The actual knowledge of the chemical reactivity is based on quantum mechanical first principles, and the complete construction of the PES represents a very important challenge in theoretical chemistry. For small reactive systems (three or four atoms), the PES construction is a relatively mature field, although even today new surfaces are still being developed for atom-diatom systems [_{2} system,

The extension to larger reactive systems (more than 4 atoms) is an open and promising field, although computationally very costly. Thus, for polyatomic systems of _{4} hydrogen abstraction reaction 10^{12} evaluations would be needed. This implies too much computer time to perform ^{−1}) and becomes totally unaffordable if one aims to achieve spectroscopic accuracy (1 cm^{−1}).

The accuracy of the kinetics and dynamics description of a chemical reaction depends, aside from the quality of the PES, on the dynamics method used. If the motion of the nuclei on the PES is determined by the Hamilton equations in the phase-space configuration, the dynamics methods are classical or quasiclassical trajectory (QCT) approaches [

In sum, electronic structure theory, dynamics methods, and constructed potential energy surfaces are the keystones of the theoretical study of chemical reactivity. Recent years have seen a spectacular development in these strongly related disciplines, paving the way towards chemical accuracy in polyatomic systems and toward spectroscopic accuracy in smaller problems. The scope of this paper is the construction of potential energy surfaces for bimolecular gas-phase polyatomic reactive systems in their electronic ground-state. Section _{4} benchmark polyatomic system and the H + NH_{3} reaction, which permits us to compare results from different methods. Section

The construction of potential energy surfaces in reactive systems began with the dawn of Quantum Chemistry when different quantum approaches were used, basically empirical or semiempirical. In present days, the data needed for this construction are obtained from high-level

As is well known, and this special issue is a clear indication of it, the construction of PESs has a long tradition in theoretical and computational chemistry, and an exhaustive review of the literature is beyond the scope of the present paper (see, for instance, a recent review in [

The most straightforward procedure to describe a reactive system is from electronic structure calculations carried out “on the fly,” sometimes also called “direct dynamics” [^{−1} below the benchmark value, the

The alternative to direct dynamics calculations is to construct a mathematical PES, that is, developing an algorithm that can provide the potential energy for any given geometry of the system without depending on “on-the-fly” electronic structure computations. In this sense, three basic approaches have been considered: fitting, interpolation, or analytical (defined by functional forms). In fact, the fitting and analytical procedures share the idea of functional form, and this analytical function needs to be fitted to theoretical information. This classification is therefore arbitrary, and other possibilities can be found in the literature [_{4} gas-phase reaction has been developed by Collins by interpolation of 30000 data points obtained with high-level

Fitting methods, such as the interpolated ones considered above, have been widely used in the construction of potential energy surfaces [_{5}^{ +} polyatomic system [^{−1}. Bowman and coworkers have developed 16 of such PESs for polyatomic systems, and they have been recently revised [

The third alternative consists of the analytical surfaces defined by functional forms. In this method the

The first surfaces were developed for the H + CH_{4} hydrogen abstraction reaction, as a paradigm of polyatomic systems [

The stretching potential is the sum of four London-Eyring-Polanyi (LEP) terms, each one corresponding to a permutation of the four methane hydrogens:_{i} stands for one of the four methane hydrogens, and H_{B} is the attacking H atom. Although the functional form of the _{i} bonds,

One of the problems with this functional was that the equilibrium C–H distances for the reactants, saddle point, and products are the same, leading to a very rigid surface. Chakraborty et al. [_{2}H_{6} reaction, included a modification to endow the surface with greater flexibility. The reference C–H bond distance is transformed smoothly from reactant to product using the following equation:

The

The reference angles are also allowed to change from their value at methane,

The _{i} bond and a vector perpendicular to the plane described by the

In the case of the H + CH_{4} reaction the CH_{3} radical product is planar. What happens if the product presents a nonplanar geometry? In these cases of CX_{3} products, we have modified the reference angle _{3}, this correction would add new parameters in the fitting procedure.

The PES, therefore, depends on at least 36 parameters, 16 for the stretching, 16 for the harmonic term, and 4 for the out-of-plane potential. These 36 parameters give great flexibility to the PES, while keeping the VB/MM functional form physically intuitive.

In the case of the H + CH_{4} reaction the CH_{4} reactant presents _{4} reaction cannot be applied without modification to any kind of system. Thus, when this potential is applied to the study of the H + NH_{3} → H_{2} + NH_{2} reaction, a major drawback was observed [_{3} inversion reaction, predicting that the planar ammonia (^{−1} more stable than the pyramidal structure (

In the original expression for the H + CH_{4} reaction (^{−1}. However, Yang and Corchado [

In sum, starting from a basic functional form, this form must be adapted to each particular case, looking for the greatest flexibility and suitability for the problem under study. This has been the main aim of the modifications on the original functional form (

Once the functional form is available, the fitting procedure is started. A very popular approach for fitting a function is the least-squares method, which, using some local optimization algorithm, gives values of the parameters that minimize (locally) the function

One must note, however, that any fitting procedure has certain limitations. First, due to the large number of parameters, it is very hard to find a global minimum for the fit, which accurately describes the entire surface. Second, due to the nature of the linear least-square method, the result is dependent on the initial parameters; third, since we use a mathematical approach without physical intuition, one usually obtains a number of distinct sets of mathematical parameters, all equally probable and good at reproducing the complete system. To make matters worse, as noted by Banks and Clary [

To solve at least partially some of the above problems, we adopt a different approach [

This strategy presents certain advantages over other methods. The first is transferability of the functional form and the fitted parameters. Since one can regard VB/MM as some kind of highly specific MM force field, it can be expected that some of the fitting parameters are transferable to a similar system, although obviously the parameter values are system specific. In our group we have used this feature to obtain, for example, the PES for the F + CH_{4} reaction [_{4} [

Thus, our research group has developed economical alternatives for constructing analytical PESs of polyatomic systems, which basically are VB/MM-type surfaces. This strategy of seeking an optimal tradeoff of time and computational cost has been successfully used in several gas-phase hydrogen abstraction reactions of five [

The FORTRAN codes and the fitted parameters of the polyatomic potential energy surfaces developed by our group are available, free of charge, for the scientific community, and can be downloaded from the POTLIB library [

The gas-phase H + CH_{4} → H_{2} + CH_{3} hydrogen abstraction reaction, as well as its deuterated isotopomers, is the prototype polyatomic reactive system and has been widely studied both theoretically and experimentally [

We will focus attention, except otherwise stated, on the three most recent and accurate surfaces for this reactive system, which were constructed with different strategies. Chronologically, in 2006 Zhang et al. [^{−1}. The three surfaces present a colinear saddle point, 180.0°, with a similar barrier height, with small differences, ±0.2 kcal mol^{−1}, that is, within the chemical accuracy, and very close to the best estimation predicted at the CCSD(T)/aug-cc-pVQZ level, 14.87 kcal mol^{−1} [

The best macroscopic measure of the accuracy of a potential energy surface is probably the rate constant, at least in the thermal bottleneck region. When we compare different dynamics methods using the same surface, the dynamics approach is tested, and when we compare theoretical and experimental results, both the dynamics method and the surface are tested. Figure

Next, we analyze some dynamics properties where different surfaces have been used and compared with the sparse experimental data. We focus on the H + CD_{4} → HD + CD_{3} reaction because there is more experimental information available for comparison. The product energy partitioning has been experimentally obtained by Valentini’s group. [

The product angular distribution is, doubtless, one of the most sensitive dynamics features with which to test the quality of the potential energy surface, but experimentally it is very difficult to measure in some cases. When the Photoloc technique is used, the laboratory speed depends on both the scattering angle and the speed of the CD_{3} product, which is influenced by the HD coproduct internal energy distribution. Uncertainties in this quantity could produce errors in the scattering angle.

Camden et al. [_{4} gas-phase reaction using the Photoloc technique. They found that the CD_{3} products are sideways/forward scattered with respect to the incident CD_{4}, suggesting a stripping mechanism (note that in the original papers [_{3} product is measured with respect to the incident H). Later, this same laboratory [_{4} reaction at lower collision energies, ranging from 0.72 to 1.99 eV. Note that the lower value, 0.72 eV, is close to the barrier height, and consequently its dynamics will be influenced mainly by the transition-state region. Figure

This is an excellent opportunity to test the quality of the PES and the dynamics methods (Figures ^{−1} lower than the best

At higher collision energies, as they increase from 1.06 to 1.99 eV, Zhang et al. [

Note that QCT calculations on the old PES-2002 surface also predicted the subsequently experimentally observed behaviour [

Very recently, Zhou et al. [

Finally, another severe test of the quality of the PES is the study of the effect of the vibrational excitation on the dynamics. In fact, the dynamics of a vibrationally excited polyatomic reaction presents a challenge both theoretically and experimentally. Camden et al. [_{4} hydrogen abstraction reaction. They found that the excitation of the asymmetric C–H stretch mode enhances the reaction cross-section by a factor of 3.0 ± 1.5 with respect to the ground-state methane, and this enhancement is practically independent of the collision energies for the three cases analyzed—1.52, 1.85, and 2.20 eV. In the following year, 2006, two theoretical papers on this issue were published: one by Xie et al. [

CH_{5} saddle point properties.^{a}

Fitting (ZBB3)^{b} | Analytical (CBE)^{c} | Interpolated (ZFWCZ)^{d} | |
---|---|---|---|

Barrier height | 14.78 | 15.01 | 15.03 |

Geometry | |||

R(C–H′) | 1.409 | 1.390 | 1.399 |

R(H′–H_{B}) | 0.901 | 0.973 | 0.895 |

<H-C-H′ | 102.8 | 106.8 | 103.1 |

<C–H′–H_{B} | 180.0 | 180.0 | 180.0 |

Vibrational frequencies | |||

3289 | 3173 | 3223 | |

3289 | 3173 | 3223 | |

3104 | 3036 | 3073 | |

1726 | 1833 | 1784 | |

1434 | 1443 | 1442 | |

1434 | 1443 | 1442 | |

1078 | 1173 | 1115 | |

1078 | 1173 | 1115 | |

1062 | 1085 | 1062 | |

440 | 542 | 522 | |

440 | 542 | 522 | |

1320i | 1488i | 1467i |

^{−1}, geometry in ^{−1};

HD product energy partitioning and vibrational distribution (percentages) for the H + CD_{4} reaction at 1.52 eV.

Surface | HD ( | HD ( | ||
---|---|---|---|---|

Analytical^{a} | 18 | 18 | 84 | 15 |

Fitted^{b} | 22 | 18 | 78 | 22 |

Exp.^{c} | 7 | 9 | ≥95 |

Arrhenius plots of ^{3} molecule^{−1} s^{−1}) for the forward thermal rate coefficients of the H + CH_{4} reaction against the reciprocal of temperature (K), in the range 250–1000 K. Black line: MCDTH quantum calculations on the CBE surface; red line: MCDTH quantum calculations on the WWM surface; blue line: quantum calculations on the ZBB2 surface; black dashed line: VTST/MT calculations on the CBE surface; crosses: experimental values [

CD_{3} product angular distribution (with respect to the incident CD_{4}) for the H + CD_{4} → HD + CD_{3} reaction at different collision energies. (a) Experimental results from [

Quantum mechanical integral cross-section (_{4} → H_{2} + CH_{3} reaction on the CBE (black line), ZBB3 (blue line), and ZFWCZ (red line) surfaces.

The reaction of hydrogen atom with ammonia is a typical five-body reactive system, and presents a rare opportunity to study both intermolecular and intramolecular dynamics. For the intermolecular case, the gas-phase H + NH_{3} → H_{2} + NH_{2} hydrogen abstraction reaction is similar to the H + CH_{4} reaction. It presents a barrier height of 14.5 kcal mol^{−1} and a reaction exoergicity of 5.0 kcal mol^{−1}, as compared to 14.87 and an endoergicity of 2.88 kcal mol^{−1}, respectively, for the H + CH_{4} analogue. Also, the inversion of ammonia between two pyramidal structures (^{−1}, depending on the level of calculation.

Only three potential energy surfaces have been developed for the H + NH_{3} system. In 2005, Moyano and Collins [_{3} using a modified Shepard interpolated scheme based on 2000 data points calculated at the CCSD(T)/aug-cc-pVDZ level (PES1 version) or as single-point calculations at the CCSD(T)/aug-cc-pVTZ (PES2 version) level. The first and second derivatives of the energy were calculated by finite differences in the energy. Previously, in 1997, our group constructed the first surface for the hydrogen abstraction reaction exclusively, CE-1997 [_{3} inversion motion, predicting incorrectly that the planar ammonia (^{−1} more stable than the pyramidal structure (_{3} inversion, together with its semiempirical character, a new analytical potential energy surface, named EC-2009, was recently developed by our group [

We begin by analyzing the hydrogen abstraction reaction. Table ^{−1} from the

For the two surfaces, Figure

Figure

The integral cross-sections in the range 10–30 kcal mol^{−1} have been evaluated using quasi-classical trajectory (QCT) calculations on both surfaces [^{−1} and increasing with the translational energy. Unfortunately, there is no experimental data for comparison, and we think that these theoretical results might stimulate experimental work on this little studied system.

Finally, the angular distributions of the H_{2} product with respect to the incident H atom has only been determined using the EC-2009 surface [^{−1}. At 25 kcal mol^{−1}, the scattering distribution is in the sideways-backward hemisphere, associated with a rebound mechanism and low impact parameters. When the collision energy increases, 40 kcal mol^{−1}, the scattering is shifted slightly towards the sideways hemisphere, due to larger impact parameters.

As was mentioned above, the EC-2009 surface describes, in addition to the aforementioned hydrogen abstraction reaction, the ammonia inversion, an example of interesting intramolecular dynamics. Figure

A very stringent test of the quality of this surface is the ammonia splitting, which demands spectroscopic accuracy. The inversion motion is represented by a symmetric double-well potential. As a consequence of the perturbation originating this double well, a splitting of each degenerate vibrational level into two levels appears, ^{−1}. Figure ^{−1} give rise to a factor of four in the computed splitting. With respect to the effect of isotopic substitution, for the ND_{3} case we obtain a value ^{−1}. Although this is greater than the experimentally reported value, 0.05 cm^{−1} [

NH_{4} hydrogen abstraction saddle point properties.^{a}

Interpolated (MC) | Analytical (EC-2009) | ||
---|---|---|---|

Barrier height | 14.64 | 14.48 | 14.73 |

Geometry | |||

R(N–H′) | 1.323 | 1.279 | 1.308 |

R(H′–H_{B}) | 0.900 | 0.868 | 0.890 |

<C–H′–H_{B} | 160.8 | 180.0 | 158.4 |

Vibrational frequencies | |||

3450 | 3444 | 3478 | |

3350 | 3373 | 3384 | |

2057 | 1861 | 1888 | |

1527 | 1623 | 1566 | |

1174 | 1497 | 1280 | |

1047 | 1080 | 1063 | |

650 | 622 | 677 | |

629 | 581 | 506 | |

1371i | 1602i | 1662i |

^{−1}, geometry in ^{−1};

Eigenvalues of ammonia inversion (in cm^{−1}).

_{2} | EC-2009^{a} | Exp.^{b} |
---|---|---|

0^{+} | 0.00 | 0.00 |

0^{-} | 3.64 | 0.79 |

1^{+} | 861.39 | 932.43 |

1^{−} | 962.90 | 968.12 |

2^{+} | 1533.36 | 1598.47 |

2^{−} | 1942.29 | 1822.18 |

^{
a}[^{b}[

Potential energy (b) and vibrational ground-state energy (a) along the reaction path of the H + NH_{3} → H_{2} + NH_{2} reaction computed using the EC-2009 (solid lines) and MC (dashed lines) surfaces. The zero of energy is set to the equilibrium potential energy of the reactants.

Arrhenius plots of ^{3} molecule^{−1} s^{−1}) for the forward thermal rate coefficients of the H + NH_{3} → H_{2} + NH_{2} reaction against the reciprocal of temperature (K) in the range 200–2000 K. Solid black line: analytical EC-2009; dashed blue line: interpolated MC; dotted red line: experimental values from [

QCT reaction cross-section (^{−1}) for the H + NH_{3} → H_{2} + NH_{2} reaction computed using the analytical EC-2009 (solid line) and interpolated MC (dashed line) surfaces.

H_{2} product angular distribution (with respect to the incident H) for the H + NH_{3} → H_{2} + NH_{2} reaction at 25 kcal·mol^{−1} (solid line) and 40 kcal mol^{−1} (dashed line), computed using QCT calculations on the EC-2009 surface.

Ammonia inversion reaction

Classical potential for the ammonia inversion path obtained from the EC-2009 surface. The first two pairs of eigenvalues are shown.

The benchmark H + CH_{4} hydrogen abstraction reaction, with five light atoms and a single heavy atom, which allows a large number of very high-level

This is a typical problem, for instance, in reactions involving halogen atoms, ^{2}P_{3/2} and ^{2}P_{1/2}, with a splitting of 404 cm^{−1} (1.1 kcal mol^{−1}), 882 cm^{−1} (2.5 kcal mol^{−1}), and 3685 cm^{−1} (3.5 kcal mol^{−1}) for F, Cl, and Br, respectively. A priori, the smaller the separation, the greater the possibility of the reaction coming from the two states, which complicates the PES construction and the dynamics study.

This problem affects all the previously described theoretical methods to develop surfaces, because it is a problem intrinsic to the initial information required: the quantum mechanical calculations. For this problem, relativistic calculations would be needed, which would immensely increase the computational cost and would make these calculations impractical in polyatomic systems. In addition, new functional forms for the analytical functions need to be developed to include the coupling between states and its dependence on coordinates [

In the case of atom-diatom reactions, some results have shed light on the spin-orbit problem, although some theory/experiment controversies still persist. For instance, for the well-studied F(^{2}P_{3/2}, ^{2}P_{1/2}) + H_{2} reaction, Alexander et al. [_{2} reaction could be well described by calculations on a single, electronically adiabatic PES, although for a direct comparison with experiment the coupling between the ground and excited s-o surfaces must be considered.

For the analogue Cl(^{2}P_{3/2}, ^{2}P_{1/2}) + H_{2} reaction, because of the larger energy separation, one would expect that the reaction could evolve on the ground-state adiabatic surface, with the contribution of the chlorine excited state, ^{2}P_{1/2}, being practically negligible according to the Born-Oppenheimer (BO) approach. However, recently a theory/experiment controversy has arisen on this issue. Thus, Lee and Liu [_{2} reaction; that is, the excited chlorine atom (Cl*) is more reactive to H_{2} than the ground-state chlorine (Cl) by a factor of at least _{2} reaction. Different laboratories [^{2}P_{3/2}) + H_{2}) will dominate the adiabatically forbidden reaction (Cl(^{2}P_{1/2}) + H_{2}). Hence, these results are in direct contrast with the experiment of Liu et al. [

In the case of polyatomic systems, this level of sophistication has not been achieved and would still be computationally prohibitive. Thus, some approaches have been considered to take into account, indirectly, the s-o effect in the construction of the PES and the dynamics study. First, for thermochemical or rate coefficient calculations, the s-o effect on the multiple electronic states is taken into account by the electronic partition function of the reactants in the usual expression^{−1}, respectively, for F, Cl, and Br. Our group considered these approaches in the construction of the surface for the F(^{2}P) + CH_{4} [^{2}P) + CH_{4} [^{2}P) + NH_{3} [^{2}P) + NH_{3} reaction, because of the presence of wells in the reactant channel (see below), this gap occurs before the system reaches the well in the region connecting the well with reactants, and its influence on the kinetics and dynamics is entirely negligible.

Schematic representation of the potential energy along the reaction path for a reaction with spin/orbit effects on the reactants. Red line: nonrelativistic calculations.

Obviously, the cost of calculating the quantum chemical information needed to build the PES increases exponentially with the number of electrons involved, and it is still a prohibitive task for large molecules and heavy atoms. Thus, for instance, while the H + CH_{4} benchmark reaction involves five light hydrogen atoms with only eleven electrons, when third-row atoms are considered, for instance, H + SiH_{4}, nineteen electrons are involved, or when larger systems are considered, for instance, H + CCl_{4}, four heavy chlorine atoms and 75 electrons must be included in the calculations. This represents an enormous computational effort, and that is prohibitive if high-level

In these complicated cases with a large number of electrons, our strategy to build the PES, based on a smaller number of _{3} [_{3} [^{2}P) + NH_{3} [_{4} [_{4} [^{2}P) + CH_{4} [^{2}P) + CH_{4} [_{4} [_{4} [_{3}Cl and Cl + CHClF_{2} [_{4} [_{4} [_{3} [^{2}P) + NH_{3} [

It is noteworthy that the functional form has remained almost unchanged, being that of the H + CH_{4} reaction, adding different modifications following the requirements of the systems under study. Thus, for the five-body systems we removed the dependency on one of the hydrogen atoms of CH_{4}, and for the seven-body system, OH + CH_{4}, we added additional Morse and harmonic terms to describe the OH bond and <HOH angle, while for the asymmetric reactions we allowed the four atoms bonded to the carbon atom to vary independently. In addition, we improved the analytical form when building the Cl + NH_{3} surface by allowing the equilibrium N–H distance to vary along the reaction path [

The last problem analyzed in this section is that associated with the presence of several maxima and minima in the polyatomic reaction. As was recently noted by Clary [

Basically, taking into account the topology of the potential energy surface and independently of whether the reaction is exothermic, endothermic, or thermoneutral, the bimolecular reactions can be classified into three broad categories (Figure

Schematic representation of the potential energy along the reaction path for different types of bimolecular reactions. R, P and C denote, respectively, reactants, products, and intermediate complexes. In all the cases, the vertical axis represents the energy and the horizontal axis the reaction coordinate.

We finish this section by describing the most complicated surface analyzed by our group [^{2}P) + NH_{3} polyatomic reaction, which presents several wells in the entry and exit channels, with a topology showed in Figure ^{−1}, and, using different correlation energy levels and basis sets, despite, they reported values in the range 4.8–6.2 kcal mol^{−1}. Xu and Lin [^{−1}, in contrast with the preceding values. Finally, we [^{−1} at the CCSD(T)/cc-pVTZ level and of 5.8 kcal mol^{−1} [^{2}P_{1/2} and ^{2}P_{3/2}, with a separation of ^{−1} ^{−1}. As discussed above, the spin-orbit coupling was taken into account in our nonrelativistic calculations in two ways: first, in the electronic partition function of the reactant (^{−1}, to the barrier height, where we have assumed that the s-o coupling is essentially fully quenched at the saddle point. With this correction, our best estimate of the barrier height was 6.6 kcal mol^{−1}.

With all this information, an analytical PES was constructed and kinetics information was obtained using VTST/MT methods [

An exhaustive dynamics study using QCT and QM methods is currently in progress in our group and should be published soon. From the results it seems that the reaction cross-sections show significant values at very low collision energies using both methodologies. In order to analyze to what extent the presence of wells (especially the well on the reactant side) is responsible for this behaviour, further studies will be carried out with a model surface similar to the Cl + NH_{3} from which the wells have been removed. Note that the latter study is possible because of the availability of an analytical surface that can be refitted to remove the wells without significantly modifying other regions of the PES, which is an added value to this kind of analytical PES. These kinds of study can help us to understand the dynamics of such a complicated system and whether transition-state theory, which (as noted above) assumes that only the saddle point region is significant, needs to be challenged.

The construction of potential energy surfaces in polyatomic reactive systems represents a major theoretical challenge, with a very high computational and human time cost. Based on high-level electronic structure calculations, fitting, interpolation, and analytical (defined by functional forms) approaches have been developed and applied in the kinetics and dynamics (classical, quasi-classical, and quantum mechanical) study of these reactions. However, in spite of the enormous progress in the last 20–30 years in theoretical algorithms and computational power, the construction of potential energy surfaces in polyatomic systems has still not reached the level of accuracy achieved for the triatomic systems.

The quality of these surfaces is still an open and debatable question, and even for the benchmark H + CH_{4} polyatomic reaction, which involves only five light hydrogen atoms and eleven electrons, small differences are found depending on the PES construction and the dynamics method. Unfortunately, the problems will increase for other important chemical systems, where some effects are present such as spin-orbit coupling, increase in the number of electrons and molecular size, or potentials with more complicated topology. In these cases, the kinetics and dynamics results will be even more strongly dependent on the quality of the PES. In the last few decades, there has been much theoretical effort on the part of various laboratories, but there is still much to do in this research field.

Throughout this paper, the emphasis has been put on the strategy developed by our group which has constructed about 15 surfaces for polyatomic systems of five, six and seven bodies. These are freely available for download from the POTLIB websites,

The analytical surfaces developed in our group are based on a basic functional form with slight modifications to suit it to each of the systems studied. In this sense, they are very specialized force fields, with mathematical functions that allow further improvements to be introduced. For example, adding terms to describe anharmonicity, mode-mode coupling, or an improved dependence of the constants of the fit on the reaction coordinate are possibilities, which can improve the functional form.

The inclusion of additional reaction channels, such as the exchange reactions in methane or ammonia, is another pending matter in work on our surfaces. This would open up the possibility of analyzing competitive channels and could lead to a better understanding of the behaviour of complex reactions.

An additional advantage of this approach is the negligible computational cost of the evaluation of the potential energy surface and its derivatives, which is a very desirable feature when one wants to apply expensive QM methods for the study of these reactions. Undoubtedly, with the evolution of computer resources, eventually a point will be reached when direct dynamics calculations using high

This work has been partially supported in recent years by the Junta de Extremadura, Spain, and Fondo Social Europeo (Projects nos. 2PR04A001, PRI07A009, and IB10001). One of the authors (M.Monge-Palacios) thanks Junta de Extremadura (Spain) for a scholarship.

^{+}+ H reaction at the full configuration interaction level

^{+}+ CO system

_{2}and Mu + F

_{2}reactions on a new

_{2}and rate constants for the H + HBr → H

_{2}+ Br abstraction reaction

_{2})

_{5}potential energy surface

_{2}: vibrational and zero-point energy effects on quasiclassical trajectories

_{4}→ H

_{2}+ CH

_{3}

^{1}D)+H

_{2}(

^{1}

_{5}

_{4}) and (T* + CD

_{4}) systems

_{3}+ H

_{2}

_{4}+ H

_{3}+ H

_{2}

_{4}+ H reaction: calibration and calculations of rate constants and kinetic isotope effects by variational transition state theory and semiclassical tunneling calculations

_{4}+H → CH

_{3}+ H

_{2}

_{2}H

_{6}reaction

_{3}

_{4}potential energy surface

_{3}→ H

_{2}+ NH

_{2}reaction

_{3}+ H → NH2 + H

_{2}hydrogen abstraction and the ammonia inversion reactions

_{4}→ HCl + CH

_{3}on an ab initio potential

_{4}. I. New analytical potential energy surface based on fitting to ab initio calculations

_{4}hydrogen abstraction reaction. Kinetics and dynamics study

_{4}+ H hydrogen abstraction reaction: thermal rate constants and kinetic isotope effects

_{3}+ H

_{2}+ H

_{2}reaction: application of variational transition-state theory and analysis of the equilibrium constants and kinetic isotope effects using curvilinear and rectilinear coordinates

_{3}+ F → NH

_{2}+ FH. Application of variational transition state theory

_{4}+ H → SiH

_{3}+ H

_{2}reaction: potential energy surface, rate constants, and kinetic isotope effects

_{4}+ O(

^{3}P) → CH

_{3}+ OH reaction. Thermal rate constants and kinetic isotope effects

^{2}P) + CH

_{4}hydrogen abstraction reaction: kinetics and dynamics

_{4}→ HCl + CH

_{3}

_{4}→ HCl + CH

_{3}reaction

_{3}+ HBr → CH

_{4}+ Br hydrogen abstraction reaction: thermal and state-selected rate constants, and kinetic isotope effects

_{4}+ H → CCl

_{3}+ ClH reaction: kinetics and dynamics study

_{4}+ OH

_{4}

_{4}(

_{3}+ H

_{2}using a new ab initio potential energy surface

_{4}→ H

_{2}+ CH

_{3}reaction

_{4}+ H → CH

_{3}+ H

_{2}reaction: full-dimensional and reduced dimensionality rate constant calculations

_{4}→ H

_{2}+ CH

_{3}on a recent potential energy surface

_{4}, CH

_{3}+ H

_{2}, and CH

_{4}dissociation at high temperature

_{4}→ HD(

_{3}reaction

_{4}→ CD

_{3}+ HD

_{4}abstraction reaction dynamics: excitation function and angular distributions

_{4}→ HD + CD

_{3}reaction

_{4}→ HD + CD

_{3}reaction

_{4}. II. Theoretical investigation of the kinetics and dynamics

_{4}reaction

_{4}reaction

_{3}+ H and deuterated analogues

_{3}reaction over a wide temperature range

_{3}

_{3}

^{14}ND

_{3}and

^{15}ND

_{3}

_{2}reaction based on a full ab initio description of the open-shell character of the F(

^{2}P) atom

_{2}reaction

^{2}P) with H

_{2}

^{2}P) + H

_{2}(v = 0,j): effects of spin-orbit and rotational states

_{2}/D

_{2}/HD reactions

_{2}→ HCL + H reaction

^{2}P) + H

_{2}reactions

^{2}P) + H

^{2}reaction

_{2}reaction probed by

^{2}P) with

_{2}

_{3}hydrogen abstraction reaction: the role of the intermediate complexes

_{3}+ Cl → NH

_{2}+ HCl: application to the kinetics study

_{4}+ H → GeH

_{3}+ H

_{2}reaction: thermal and vibrational-state selected rate constants and kinetic isotope effects

_{4}→ HCl(

_{3}reaction

_{3}Y + A → products

_{3}reactions with ClOx (x = 0-4) radicals